By the Giambruno-Zaicev theorem for associative p.i. algebras, the exponential rate of growth of the codimensions of such a p.i. algebra is always a positive integer. Here we calculate that integer for various generic p.i. algebras which are given by a single identity. These include Capelli-type id
The exponential growth of codimensions for Capelli identities
β Scribed by S. P. Mishchenko; A. Regev; M. V. Zaicev
- Publisher
- The Hebrew University Magnes Press
- Year
- 2000
- Tongue
- English
- Weight
- 346 KB
- Volume
- 115
- Category
- Article
- ISSN
- 0021-2172
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π SIMILAR VOLUMES
Let F be a field of characteristic zero and let A be a finite dimensional algebra with involution ) over F. We study the asymptotic behavior of the sequence of n Ε½ . Ε½ . )-codimensions c A, ) of A and we show that Exp A, ) s lim c A, ) ' Ε½ . n n Βͺ Ο± n Ε½ . exists and is an integer. We give an expli
Let A be an associative PI-algebra over a field F of characteristic zero. By studying the exponential behavior of the sequence of codimensions [c n (A)] of A, we prove that Inv(A)=lim n Γ n c n (A) always exists and is an integer. We also give an explicit way for computing such integer: let B be a f